FAST: blade root flap and edge moments

Hi, all.

I was wondering how the blade root flap-wise and edge-wise moments (RootMyb# and RootMxb#, respectively) are calculated in FAST. It seems they are not mere linear combinations of blade root in-plane moments and out-of-plane moments (RootMxc# and RootMyc#, respectively).

I was expecting the following relations but FAST seems to involve more complex calculations:
M_flap = M_oop * cos(pitch) – M_ip * sin(pitch)
M_edge = M_oop * sin(pitch) + M_ip * cos(pitch)
, where M_flap = blade root flap-wise moment, M_edge = blade root edge-wise moment, M_ip = blade root in-plane moment, M_oop = blade root out-of-plane moment, pitch = collective blade pitch angle

I would truly appreciate it if anyone kindly teach me regarding this matter.

Best,
Youngjun

Dear Youngjun,

The equations in your post relating the root flapwise and edgewise bending moments with the root out-of-plane and in-plane bending moments are correct. What led you to believe they are not correct?

Best regards,

Dear Dr. Jonkman,

Thank you very much for your quick response.
Since there was a small difference between the values calculated outside of FAST according the equations and the values generated from FAST, I wanted to make sure whether the equations were correct. Thanks to you, now I can conclude that the small difference was just because of the computational error.

I truly appreciate your help again !

Sincerely,
Youngjun

Dear Dr. Jason Jonkman,

I hope all is well with you. It’s been almost 4 years since I opened this thread.

Previously, I thought that the discrepancies between the calculated values (M_edge or M_flap) and FAST outputs (RootMxb# or RootMyb#) were due to numerical error, because the magnitudes were small.

Today, I compared those values again when 10-min avg. wind speed is 25 m/s (previously, it seems I used a smaller speed). It turned out that the range of observed M_edge (calculated using RootMxc1 and RootMyc1) in 10-min is (-4844, 10265) kNm for one instance. On the other hand, the observed range of RootMxb1 is (-5099, 5181) kNm.

The reason that I started investigating the discrepancy is that the ranges of edgewise bending moments reported in the following two papers are noticeably different although the setups are almost identical:

• Moriarty, P. (2008). Database for validation of design load extrapolation techniques. Wind Energy, 11(6), 559.
• Barone, M., Paquette, J., Resor, B., & Manuel, L. (2012). Decades of wind turbine load simulation. In Proceedings of the 50th AIAA Aerospace Sciences Meeting.
The main difference between the two papers’ setups appears to be that the former paper used the calculated M_edge while the latter paper likely used the direct output from FAST.

I would greatly appreciate it if you could shed light on understanding the discrepancy. Thank you in advance for your time looking into this!

Dear Youngjun,

I looked back at your equations and indeed found an error. The correct transformation between the root out-of-plane and in-plane bending moments and the root flapwise and edgewise bending moments is as follows:

M_flap = M_oop * cos(pitch) + M_ip * sin(pitch)
M_edge = -M_oop * sin(pitch) + M_ip * cos(pitch)

My guess is I originally misread your post as pertaining to shear forces, whereby your transformation is correct. That is, the transformation between the root out-of-plane and in-plane shear forces and the root flapwise and edgewise shear forces is as follows:

F_flap = F_oop * cos(pitch) – F_ip * sin(pitch)
F_edge = F_oop * sin(pitch) + F_ip * cos(pitch)

I haven’t looked at the papers you referenced, but does the use of these corrected transformations produce the results you expect?

Best regards,

Dear Dr. Jason Jonkman,

Thank you so much for your prompt help.

I confirmed that the corrected transformations indeed produce M_flap and M_edge agreeing well with RootMyb1 and RootMxb1 generated from FAST, respectively.

The general pattern of edgewise bending moments (RootMxb1) was somewhat surprising to me, because I used to see that edgewise bending moments generally increase as wind speed increases in data from actual turbines of different models. Would you kindly take a look at the attached pdf file where I copied and pasted the figures from the two papers, which perplexed me? I was wondering which figure looks more right to you based on your experience with the onshore version of the 5 MW NREL reference turbine. I would greatly appreciate your insight on this.

Best Regards,
Youngjun
Comparison of edgewise bending moments from two papers.pdf (224 KB)

Dear Youngjun,

I was not involved in either of those papers, but I would guess that what is plotted in Barone et al (2012) is correctly the blade-root edgewise-bending moment and what is plotted in Moriarty (2008) is the blade-root in-plane-bending moment (or an incorrectly transformed edgewise moment). Indeed, the transformation between out-of-plane/in-plane moments and flapwise/edgewise moments is identified incorrectly in Moriarty (2013).

Best regards,

Dear Dr. Jason Jonkman,

Thank you so much for your time helping me on this issue. I believe everything is cleared now. Thank you!

Best Wishes,
Youngjun